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A rope of length L and mass m hangs free...

A rope of length L and mass m hangs freely from the ceiling. The velocity of transverse wave as a function of position x from the bottom is proportional to

A

T

B

`T((sqrt(2)-1)/(sqrt(2)))`

C

`(T)/(sqrt(2))`

D

`(T)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • A rope of length L and mass m hangs freely from the ceiling. The velocity of transverse wave as a function of position x along the rope is proportional to

    A
    `x^(0)`
    B
    `sqrt(x) `
    C
    `(1)/(sqrt(x))`
    D
    `x `

  • A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

    A
    `sqrt(gL)`
    B
    `sqrt(gx)`
    C
    gL
    D
    gx

  • A uniform rope of mass 0.1 kg and length 2.5 m hangs from ceiling. The speed of transverse wave in the rope at upper end at a point 0.5 m distance from lower end will be

    A
    `5" ms"^(-1) and 2.24 "ms"^(-1)`
    B
    `10" ms"^(-1) and 3.23 "ms"^(-1)`
    C
    `7.5" ms"^(-1) and 1.2 "ms"^(-1)`
    D
    None of these

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